In the conventional method for nesting multiple concentric pipes of different diameters b (hereinafter nested pipes b) into an existing pipe a, the tail end f of the inner pipe d of the nested pipes b must protrude from the tail end e of the outer pipe c of said nested pipes b. The reason is that a new section of the inner pipe d is first welded at joint g onto the section of the inner pipe d already inserted, next a section of the outer pipe c is welded at joint g onto the outer pipe c, then the extended nested pipes are inserted into the existing pipe a, after which the welding and insertion is repeated until the nested pipes are fully inserted. For this, in order that sections of inner pipe d can be welded together, its tail end f must protrude from the tail e of the outer pipe c. However, in this case, the plug of the thrusting device, not shown in the diagram, cannot be mounted inside the tail end e of the outer tube c. Accordingly, the outer pipe c cannot be filled with a filler fluid h upon which a pressure can be imparted by a thrusting device to push the nested pipes b into the existing pipe a.